God May Be Maximally Simple

Why the prior probability of God is high

Theists inevitably think that ultimate reality is a foundational mind of limitless power, knowledge, and goodness. Atheists instead generally think that ultimate reality is a set of lawful equations, followed all throughout the universe, perhaps conjoined with fundamental psychophysical laws.

When evaluating a hypothesis, there are various theoretical virtues that one ought to take into account. These affect its prior probability—how likely a theory is before you look at the evidence. Both the theory that Bob is cheating in poker and that a fairy rigged the deck explain him getting ten royal flushes, but the cheating hypothesis has a higher prior.

I don’t have an exhaustive list of all the theoretical virtues, but in my view three important ones are simplicity (how few things a theory posits at the fundamental level), elegance (whether the things that it posits as fundamental are contrived and arbitrary), and modesty (how much the theory requires to be true of the world). For example, string theory is simple (strings are easy to mathematically describe), elegant (the strings aren’t particularly weird and arbitrary), but not at all modest, because it requires something very specific to be true. Any maximally specific version of string theory can only be true in one way, while it can be false in an infinite number of ways.

Theism is quite a bit less modest than atheism—it’s a highly specific way for reality to be—and as a consequence, in order for it to have a higher prior probability than atheism, it needs to do better in terms of other virtues like simplicity and elegance.

Still, having enough simplicity and elegance to make up for great immodesty isn’t too difficult. The theory that the laws of nature are totally uniform is way more probable than the theory that the laws of nature work everywhere except in some random galaxy, even though it’s much less modest. There’s just one way for the laws to be uniform, while there are infinite ways for the laws to not be uniform.

Similarly, the hypothesis that God knows everything is much likelier than the hypothesis that God knows every fact but one. But note: there are infinity ways for God to know every fact but one, while only one way for him to know every fact. Thus, a simple and elegant theory can often massively beat out a less elegant theory.

This leads to an important takeaway: because simple and elegant theories are so much more probable than complex and non-elegant ones, if a theory has even a slight chance of being maximally simple and elegant, it’s usually better than a theory with no chance of being maximally simple and elegant, even if the second theory is on average simpler and more elegant.

To see this, let’s consider a toy model. You don’t know exactly what theory 1 says—it might say that the laws are uniform throughout the universe, or it might be infinitely complex. Let’s say theory 1 has a 1/1000 chance of holding that there are uniform laws and a 999/1000 chance of holding to laws of literally infinite complexity. Theory 2 definitely holds that the laws are uniform everywhere except in one galaxy. Because the theory that the laws are uniform has a prior more than 1000 times greater than the theory that the laws are uniform everywhere except in one galaxy, theory 1 has a much higher prior than theory 2.

Thus, when calculating priors, the thing that’s most important isn’t how simple a theory is on average—we just saw that a theory with infinite average complexity could beat a theory that’s pretty simple on average—but the theory that has the best claim to being the simplest theory. The overwhelming majority of prior probability space is occupied by the very simplest theory.

Put this way, naturalism doesn’t do great in terms of priors. Sure, it’s probably pretty simple. But the mathematical laws take many symbols to describe—far less parsimonious than some much simpler mathematical laws that wouldn’t give rise to anything interesting. Because naturalism doesn’t have a nice claim to being the simplest theory, it’s relevantly analogous to the theory that the laws are uniform everywhere except one patch—maybe pretty simple, but easily beaten out by the very simplest and most elegant theories.

In contrast, I think theism has a very good claim to being the very simplest theory there is. I’ll tell one story of how this might be—how God’s properties all follow from one utterly simple property—but this is by no means the only account. Elsewhere, I’ve listed 10 such accounts, and while I have doubts about many of them, I think it’s pretty likely that one of them works: candidate essential properties that may entail all the rest of God’s properties include perfection, limitless being, pure act, limitless value, limitless agency, limitless volitional will, a mind of limitless power, an omnipotence trope, and more. In particular, I find limitless agency plausibly fundamental—agency is a match between a mind and the world. Limitless agency involves the mind being perfectly mirrored in reality (omnipotence) and reality being fully mirrored in the mind (omniscience).

My preferred view is that God is essentially a limitless mind or consciousness—Robin Collins has also defended this view in various places. Now, in my view, the world has three core kinds of things: minds, the material world, and abstract objects. It makes no sense to talk about a limitless material object or a limitless abstract object—besides abstract objects don’t do anything. Thus, if reality is any kind of fundamental thing instantiated without limit, it must be an unlimited mind.

If mind is fundamental, then a fundamental mind isn’t so surprising. I’ve elsewhere defended that mind is fundamental and irreducible. You might disagree with me about whether mind is fundamental, but so long as it’s remotely plausible that it is, the odds of theism being super simple aren’t terribly low. Given that lots of very smart philosophers think mind is fundamental, you shouldn’t be extremely confident that it’s not fundamental. And if there’s some nontrivial chance that theism is super simple, for reasons already described, it will probably have a much higher prior than naturalism.

So, a foundational mind isn’t terribly unlikely. But why think that the mind would be limitless? In my view, we have three fairly similar reasons:

1. Generally the simplest and most elegant way for a thing to be is simply: without limit. Which is simple and more elegant: a universe that is infinite in size or one that is exactly 32940732 meters across. Clearly the limitless one! Similarly, a mind completely without limit is more simple and elegant than one of some arbitrary size. But if a mind is totally without limit, then there is no restriction on either what it can do or what it’s aware of—thus, such a mind would be omniscient and omnipotent.

2. Given that this mind is fundamental, there are no external constraints or internal constraints. Thus, by default, it seems it would have no constraints at all—neither on what it knows nor on what it can do.

3. Limits on what something can do seem to require explanation. By default, we should have assumed there was no limit on the speed objects could reach, because that’s a limit on what things can do. But a mind without limits on what it can do would be omnipotent, and because it could bring any fact to mind at will, it would also be omniscient.

From this, the path to omnibenevolence is straightforward. A totally limitless mind would know all the moral facts—recognizing, in all cases, what it ought to do. But it’s quite plausible that if you have no rational inhibition or conflicting desire and recognize that something is worth pursuing, you’ll be motivated to pursue it (for a more in depth defense, see here). Just as reason compels you to value your future self—e.g. a perfectly rational person wouldn’t procrastinate or jeopardize their future interests for present gain—reason compels you to care about others. Again, you don’t have to think this is certain, just not horrendously implausible, for theism to have a decent prior.

Now, my biggest worry about this: maybe being limitless isn’t a joint carving property (credit to my friend who writes the non-natural facts blog for this objection). The fact that we have a single word for a concept—limitless—doesn’t make it fundamental. We have one word for America, but that doesn’t mean America is simple or could be easily instantiated. Other cases where limitless properties are simple just involve those properties being maximally instantiated—but a mind is a thing, not a property, and thus can’t be maximally instantiated. In response, I’d note a few things:

1. This only really addresses the first point. The second points aren’t about limitless as a fundamental property, but instead about the default lack of constraints on a mind. Thus, even if this is right, a fundamental mind could still be plausible.

2. There isn’t a knockdown argument for either thinking limitless is or isn’t joint carving and fundamental. Given this, it seems we should think it might be fundamental or might not—but then a limitless mind being simple remains somewhat plausible.

3. Intuitively, it really just seems like it’s fundamental! Just as modal realism seems simple—simply possible worlds instantiated without limit—it seems a mind without limits is simple and fundamental. Reasonable minds can differ here, of course, but this is how it seems to me. Being limitless just does seem joint-carving! It relates to whether a thing is bounded in any respect. If a mind isn’t bounded at all, it will have fully efficacious will and total awareness of anything. Everything is limited with regard to a bunch of arbitrary functions—e.g. if you take a function which assigns a score of infinity to anything with finite size and 0 to anything with infinite size, an infinitely large world is limited with regard to its score on the function. Similarly, any time that something is limitless, it can’t be thought of as an infinite disjunct of other limitless properties—being limitless in size involves having no limit to the extent to which something fills any individual unit of space. But a limitlessly sized entity isn’t arbitrary because it’s unbounded with regard to a more fundamental property—there’s something arbitrary about a thing with a finite size, even though a thing with infinite size is bounded with respect to various arbitrary functions. Similarly, there seems something arbitrary about a fundamental mind that can’t achieve certain tasks or that’s ignorant—it seems bounded or restricted.

4. I worry that the analysis that holds that when we call something fundamental that’s just a short way of saying that some property is instantiated without limit is inadequate. It can’t explain why a universe of limitless size has a higher prior than one that’s 3190438 meters across. Both take equally long to describe. Holding limitless as a kind of primitive explains this—you can simply use one symbol to describe the laws being instantiated without limit. Similarly, modal realism seems simple, even though it’s a maximal instantiation of a kind of thing not a property.

5. Worst case scenario, theism can be defined as the hypothesis that there’s a mind of limitless power. Power—ability to do stuff—is plausibly fundamental. So then theism will still be quite simple and elegant, far more than naturalism!

All in all, I think this is a complicated subject. I don’t quite know what to think about it! But I think theism has a plausible case for being the very simplest way that reality could be—this is the view I lean towards. Thus, taking into account uncertainty, one’s prior in theism should be pretty high overall—especially because this is just one route of many towards a simple God, and as discussed before, the odds of theism being the simplest and most elegant theory matter a lot more than its average degree of simplicity elegance.

However, I find this subject complicated enough that I wouldn’t put all my eggs in the priors basket. Because of my uncertainty, I think one’s priors shouldn’t be extreme—neither near certainty of theism nor of atheism. If you agree these subjects are tricky and complicated, then you shouldn’t start with a prior in theism well below one in a thousand. So long as you keep your priors non-extreme, your probabilities will mostly be dictated by the mountain of evidence favoring theism. Atheists will probably disagree that the evidence massively favors theism—in any case, I don’t think their overall judgment of theism’s likelihood should hinge too much on its priors.